Question

X的概率密度为fx(x),则Y=-2X+3的概率密度

Answer 1

Y=-2X+3=》X=(3-Y)/2

FY(y)=P(Y=-2X+3)=P(X=3/2-Y/2)

fY(y)=[F'Y(y)]=[FX(3/2-Y/2)]'=fX(3/2-Y/2)*(3/2-Y/2)'=-1/2*fX(3/2-Y/2)